This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364422 #23 Sep 30 2023 21:41:16
%S A364422 0,0,2,12,120,1200,14400,191520,2862720,47174400,852768000,
%T A364422 16765056000,356377190400,8144943206400,199202395392000,
%U A364422 5191467240960000,143634952581120000,4204936774950912000,129865748246986752000,4219868533182382080000,143918318293689139200000
%N A364422 Expansion of e.g.f. x^2/(1-x-x^2)^2.
%C A364422 a(n) is the number of ways to partition [n] into blocks of size at most 2, order the blocks, order the elements within each block, and choose 2 elements from a block.
%F A364422 a(n) = A000142(n)*A001629(n).
%e A364422 a(6)=14400 since the number of ways to partition [6] into blocks of size at most 2, order the blocks, order the elements within each block, and select 2 elements from a block are the following:
%e A364422 (i) 12,3,4,5,6: 3600 such orderings, 1 way to choose 2 elements (from the block with 2 elements), hence 3600 ways;
%e A364422 (ii) 12,34,5,6: 4320 such orderings, 2 ways to choose 2 elements (from one of the two blocks with 2 elements), hence 8640 ways.
%e A364422 (iii) 12,34,56: 720 such orderings, 3 ways to choose 2 elements (from one of the three blocks with 2 elements), hence 2160 ways.
%t A364422 With[{m = 20}, Range[0, m]! * CoefficientList[Series[x^2/(1 - x - x^2)^2, {x, 0, m}], x]] (* _Amiram Eldar_, Sep 02 2023 *)
%Y A364422 Cf. A000045, A000142, A001629, A005442.
%K A364422 nonn
%O A364422 0,3
%A A364422 _Enrique Navarrete_, Sep 01 2023